If f x is continuous and f 9 2 = 2 9 , then lim x → 0 f 1 - cos 3 x x 2 equals to

Step-by-step solution

Given: f 9 2 = 2 9 and f x is continuous. lim x → 0 f 1 - cos 3 x x 2 = f lim x → 0 1 - cos 3 x x 2 = f lim x → 0 2 sin 2 3 x 2 x 2 ∵   1 - cos 2 θ = 2 sin 2 θ = f lim x → 0 2 sin 2 3 x 2 4 9 3 x 2 2 = f 9 2 lim x → 0 sin 2 3 x 2 3 x 2 2 = f 9 2 × 1 2 ∵     lim x → 0 sin x x = 1 = f 9 2 = 2 9